Optimization of finite plates with polygonal cutout under in-plane loading by gray wolf optimizer

Abstract

This article investigates the optimum design of isotropic finite plates with different polygonal cutouts under in-plane loading (uniaxial tensile, biaxial, and pure shear load). This purpose is pursued by a gray wolf optimization algorithm. The important features of this algorithm include flexibility, simplicity, short solution time, and the ability to avoid local optimums. The objective function used for this algorithm seeks to minimize the value of stress concentration factor around different cutouts. The method used for the calculation of stress concentration is based on analytical solution of Muskhelishvili complex variable and conformal mapping with plane stress assumption. The plate is assumed to be isotropic, linear elastic, and finite (the ratio of cutout side to plate’s longest side in the square and triangular cutouts and the ratio of diameter of circle circumscribing other n-gonals to the plate’s longest side are greater than 0.2). Results show that by selecting the aforementioned parameters properly, less amounts of stress could be achieved around the polygonal cutout leading to an increase in load-bearing capacity of the structure.